Relative periodic orbits in point vortex systems

Nonlinearity

Volumn 17, Issue 6, 2004, Pages 1989-2013

  Laurent Polz, F ^a  

^a UNIVERSITÉ CÔTE D'AZUR   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 9544231654     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/17/6/001     Document Type: Article

References (24)

1. [Ar82] Aref H 1982 Point vortex motion with a center of symmetry Phys. Fluids 25 2183-7
2. [Ar83] Aref H 1983 The equilibrium and stability of a row of point vortices J. Fluid Mech. 290 167-81
3. [AV98] Aref H and Vainchtein C 1998 Asymmetric equilibrium patterns of point vortices Nature 392 769-70
4. [ANSTV] Aref H, Newton P, Stremler M, Tokieda T and Vainchtein D L 2003 Vortex crystals Adv. Appl. Mech. 39 1-79
5. [BC03] Boatto S and Cabral H 2003 Non-linear stability of relative equilibria of vortices on a non-rotating sphere SIAM J. Appl. Math 64 216-30
6. [CS99] Cabral H and Schmidt D 1999 Stability of relative equilibria in the problem of N + 1 vortices SIAM J. Math. Anal. 31 231-50
7. [H] Helmholz H 1867 On integrals of the hydrodynamical equations which express vortex motion Phil. Mag. 33 485-512
8. [KN98] Kidambi R and Newton P 1998 Motion of three point vortices on a sphere Physica D 116 143-75
9. [LMR01] Lim C, Montaldi J and Roberts M 2001 Relative equilibria of point vortices on the sphere Physica D 148 97-135
10. [LMR] Laurent-Polz F, Montaldi J and Roberts M Stability of relative equilibria of point vortices on the sphere Physica D submitted
11. [LP02] Laurent-Polz F 2002 Point vortices on the sphere: a case with opposite vorticities Nonlinearity 15 143-71
12. [LP] Laurent-Polz F 2002 Point vortices on a rotating sphere Preprint INLN math.DS/0301360
13. [LPth] Laurent-Polz F 2002 Etude Géométrique de la Dynamique de N tourbillons Ponctuels sur une Sphère PhD Thesis University of Nice
14. [LR96] Lewis D and Ratiu T 1996 Rotating n-gon/kn-gon vortex configurations J. Nonlinear Sci. 6 385-414
15. [LT99] Lerman L and Tokieda T 1999 On relative normal modes C. R. Acad. Sci., Paris 1328 413-8
16. [Mo97] Montaldi J 1997 Persistence d'orbites périodiques relatives dans les systèmes Hamiltonien symétriques C. R. Acad. Sci., Paris I 324 553-8
17. [MR94] Marsden J and Ratiu T 1994 Introduction to Mechanics and Symmetry (TAM vol 17) (Berlin: Springer)
18. [Or98] Ortega J-P 1998 Symmetry, reduction, and stability in Hamiltonian systems PhD Thesis University of California, Santa Cruz
19. [Or03] Ortega J-P 2003 Relative normal modes for nonlinear Hamiltonian systems Proc. R. Soc. Edinb. A 133 665-704
20. [P79] Palais R 1979 Principle of symmetric criticality Commun. Math. Phys. 69 19-30
21. [PM98] Pekarsky S and Marsden J 1998 Point vortices on a sphere: stability of relative equilibria J. Math. Phys. 39 5894-907
22. [ST] Soulière A and Tokieda T 2002 Periodic motions of vortices on surfaces with symmetry J. Fluid Mech. 460 83-92
23. [To01] Tokieda T 2001 Tourbillons dansants C. R. Acad. Sci., Paris I 333 943-6
24. [WR02] Wulff C and Roberts M 2002 Hamiltonian systems near relative periodic orbits SIAM J. Appl. Dyn. Syst. 1 1-43